TOPIC-01 · Engineering guide
Ideal Transformer Turns and Voltage Ratio
In this ideal model, winding-phase voltages are in the same ratio as the turns. With N1 = 100, N2 = 10 and V1 = 230 V, V2 = 23 V and N1/N2 = 10.
Formula, variables and conditions
Winding-phase voltages: V1 / V2 = N1 / N2. A wye line-to-line voltage is divided by sqrt(3) before that ratio. A delta line-to-line voltage is already the winding voltage.
Variables and units
- N1, N2: turn counts, positive integers.
- V1, V2: voltages in V, kV or mV after the declared unit factor.
- Voltage mode: winding-phase or line-line, declared on each side.
- Connection: single for single-phase; wye or delta for balanced three-phase.
Conditions
- Solve-voltage-ratio needs N1, N2 and V1. V2 is the output.
- Solve-turns-ratio needs V1 and V2. The turns are the output ratio, not a winding design.
- Single-phase requires the single connection on both sides.
- The stored model is TOOL-021 model 1.1.0, formula F-TR-001, source SRC-058.
Worked example
This is the locked single-phase teaching fixture. Both sides are winding-phase and the connection is single.
- Solve mode
- solve-voltage-ratio
- N1 / N2
- 100 / 10
- V1
- 230 V
- V2
- 23 V
- Turns ratio N1/N2
- 10
- Reverse check
- V1 = 230 V and V2 = 23 V returns the ratio 10
The ideal magnitude ratio is exactly 10, so 230 V on the primary winding corresponds to 23 V on the secondary winding.
Boundaries and common mistakes
Boundaries
- No impedance drop, voltage regulation, vector-group phase shift, taps or unbalance.
- The OpenStax page supports the ideal induction relation. It is not an equipment rating.
- Passing this arithmetic does not select a transformer.
Common mistakes
- Using a line-to-line wye voltage as if it were the winding voltage. The model divides that entry by sqrt(3) first.
- Treating the turns ratio as percent regulation. Regulation is a separate per-unit series model.
- Entering turns while solving for the turns ratio. That mode rejects N1 and N2.